An annuity writer sells an annual perpetuity-immediate for 16,000. The first payment is 1,000 and the payments decrease by r% each year. The annual effective yield rate is 5.7%.

Calculate r.

• 0.52
• 0.55
• 0.62
• 0.73
• 0.91

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: B

[[math]] \begin{aligned} & 16,000=1,000\left(\frac{1}{0.057-(-r / 100)}\right) \\ & 16=\frac{1}{0.057+r / 100} \\ & 0.057+r / 100=\frac{1}{16} \\ & r=0.55\end{aligned} [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.